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Efficient Frontier

Efficient Frontier Overview

This tool uses mean-variance optimization to calculate and plot the efficient frontier for the specified asset classes, mutual funds, ETFs, or stocks based on historical returns or forward-looking capital market assumptions The efficient frontier shows the set of optimal portfolios that provide the best possible expected return for the level of risk in the portfolio. Monte Carlo method can be used for more robust optimization that resamples the optimization inputs in order to mitigate the impact of input estimation errors and improve diversification. The required inputs for the efficient frontier include the portfolio assets. You can optionally specify the asset allocation and allocation constraints for the portfolio assets. If an asset allocation is specified, the provided portfolio will be rendered on the efficient frontier chart.

Efficient Frontier Configuration

Efficient Frontier Assets
Allocation
Expected Return
Volatility
Min. Weight
Max. Weight
Group
1
%
%
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2
%
%
%
%
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3
%
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4
%
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%
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5
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%
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6
%
%
%
%
%
7
%
%
%
%
%
8
%
%
%
%
%
9
%
%
%
%
%
10
%
%
%
%
%
Total
%
Asset Groups
Min. Weight
Max. Weight
A
%
%
B
%
%
C
%
%
D
%
%
E
%
%
F
%
%

Efficient Frontier Results (Jan 2017 - Sep 2026)

Note:
  • The time period was constrained by the available data for SPDR Gold Shares (GLD) [Dec 2004 - Sep 2026] and Vanguard Real Estate ETF (VNQ) [Oct 2004 - Sep 2026].
  • The time period of the results is limited to 10 years for free tier accounts.

Provided Portfolio

Ticker Name Allocation
SPY State Street SPDR S&P 500 ETF 12.50%
SLYV State Street SPDR S&P 600 Sm CpValETF 12.50%
EFA iShares MSCI EAFE ETF 12.50%
EEM iShares MSCI Emerging Markets ETF 12.50%
VNQ Vanguard Real Estate ETF 12.50%
TLT iShares 20+ Year Treasury Bond ETF 12.50%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 12.50%
GLD SPDR Gold Shares 12.50%

Max Sharpe Ratio Portfolio

Ticker Name Allocation
SPY State Street SPDR S&P 500 ETF 50.96%
SLYV State Street SPDR S&P 600 Sm CpValETF 2.75%
EFA iShares MSCI EAFE ETF 0.75%
EEM iShares MSCI Emerging Markets ETF 1.67%
TLT iShares 20+ Year Treasury Bond ETF 0.58%
LQD iShares iBoxx $ Invmt Grade Corp Bd ETF 1.45%
GLD SPDR Gold Shares 41.84%

Performance Summary

PortfolioExpected ReturnStandard DeviationSharpe Ratio
Provided Portfolio8.54%11.78%0.52
Max Sharpe Ratio Portfolio14.28%11.65%1.01

Efficient Frontier

Efficient Frontier Assets

#AssetExpected ReturnStandard DeviationSharpe RatioMin. WeightMax. Weight
1State Street SPDR S&P 500 ETF15.43%15.47%0.8370.00%100.00%
2State Street SPDR S&P 600 Sm CpValETF10.38%22.13%0.3570.00%100.00%
3iShares MSCI EAFE ETF10.12%15.07%0.5070.00%100.00%
4iShares MSCI Emerging Markets ETF10.29%17.35%0.4510.00%100.00%
5Vanguard Real Estate ETF6.30%17.75%0.2160.00%100.00%
6iShares 20+ Year Treasury Bond ETF-0.64%13.48%-0.2310.00%100.00%
7iShares iBoxx $ Invmt Grade Corp Bd ETF2.47%8.34%0.0010.00%100.00%
8SPDR Gold Shares13.99%15.31%0.7520.00%100.00%
Results based on historical returns. Expected return is the annualized monthly arithmetic mean return. Ex-ante Sharpe Ratio calculated using U.S. 3-Month Treasury Bill Rate returns as the risk-free rate.

Asset Correlations

NameTickerSPYSLYVEFAEEMVNQTLTLQDGLD
State Street SPDR S&P 500 ETFSPY1.000.800.830.690.780.190.610.15
State Street SPDR S&P 600 Sm CpValETFSLYV0.801.000.760.620.760.050.490.02
iShares MSCI EAFE ETFEFA0.830.761.000.810.750.240.670.30
iShares MSCI Emerging Markets ETFEEM0.690.620.811.000.560.230.590.38
Vanguard Real Estate ETFVNQ0.780.760.750.561.000.410.700.21
iShares 20+ Year Treasury Bond ETFTLT0.190.050.240.230.411.000.760.34
iShares iBoxx $ Invmt Grade Corp Bd ETFLQD0.610.490.670.590.700.761.000.37
SPDR Gold SharesGLD0.150.020.300.380.210.340.371.00
Based on monthly returns from Jan 2017 to Sep 2026

Efficient Frontier Portfolios

#State Street SPDR S&P 500 ETFState Street SPDR S&P 600 Sm CpValETFiShares MSCI EAFE ETFiShares MSCI Emerging Markets ETFVanguard Real Estate ETFiShares 20+ Year Treasury Bond ETFiShares iBoxx $ Invmt Grade Corp Bd ETFSPDR Gold SharesExpected Return *Standard Deviation *Sharpe Ratio *
10.90%0.24%0.00%0.00%0.00%0.00%87.95%10.91%3.87%8.22%0.170
21.12%0.28%0.00%0.00%0.00%0.00%86.79%11.81%4.00%8.22%0.186
31.44%0.32%0.01%0.01%0.00%0.00%85.68%12.55%4.13%8.23%0.202
41.83%0.34%0.01%0.01%0.00%0.00%84.62%13.19%4.26%8.24%0.217
52.28%0.35%0.02%0.01%0.00%0.00%83.58%13.75%4.38%8.25%0.232
62.77%0.37%0.03%0.01%0.00%0.00%82.55%14.27%4.51%8.26%0.247
73.28%0.40%0.03%0.01%0.00%0.00%81.51%14.77%4.64%8.27%0.262
83.82%0.41%0.04%0.01%0.00%0.00%80.47%15.25%4.76%8.28%0.277
94.38%0.43%0.05%0.01%0.00%0.00%79.43%15.71%4.89%8.30%0.291
104.95%0.43%0.05%0.01%0.00%0.00%78.40%16.16%5.02%8.31%0.306
115.54%0.43%0.06%0.01%0.00%0.00%77.36%16.60%5.14%8.33%0.321
126.14%0.43%0.07%0.01%0.00%0.00%76.32%17.03%5.27%8.34%0.336
136.74%0.44%0.07%0.01%0.00%0.01%75.28%17.46%5.40%8.36%0.350
147.35%0.44%0.08%0.01%0.00%0.01%74.23%17.88%5.53%8.38%0.365
157.96%0.44%0.09%0.02%0.00%0.01%73.18%18.31%5.66%8.40%0.379
168.57%0.44%0.09%0.02%0.00%0.02%72.13%18.72%5.78%8.42%0.393
179.19%0.45%0.10%0.03%0.00%0.02%71.08%19.14%5.91%8.45%0.408
189.82%0.45%0.10%0.03%0.00%0.03%70.02%19.55%6.04%8.47%0.422
1910.44%0.45%0.11%0.03%0.00%0.04%68.97%19.96%6.17%8.49%0.436
2011.06%0.46%0.11%0.04%0.00%0.04%67.91%20.37%6.30%8.52%0.450
2111.69%0.47%0.12%0.05%0.00%0.05%66.85%20.78%6.43%8.54%0.463
2212.31%0.47%0.13%0.05%0.00%0.07%65.78%21.19%6.56%8.57%0.477
2312.94%0.48%0.13%0.06%0.00%0.08%64.71%21.59%6.69%8.60%0.490
2413.57%0.49%0.14%0.07%0.00%0.09%63.65%22.00%6.82%8.63%0.504
2514.20%0.50%0.14%0.08%0.00%0.11%62.58%22.40%6.95%8.66%0.517
2614.82%0.51%0.15%0.08%0.00%0.12%61.51%22.81%7.08%8.69%0.530
2715.45%0.52%0.15%0.09%0.00%0.14%60.43%23.21%7.20%8.72%0.543
2816.08%0.53%0.16%0.10%0.00%0.16%59.36%23.62%7.33%8.75%0.556
2916.71%0.54%0.16%0.11%0.00%0.18%58.28%24.02%7.46%8.79%0.568
3017.34%0.55%0.17%0.11%0.00%0.21%57.20%24.43%7.59%8.82%0.580
3117.97%0.56%0.18%0.12%0.00%0.24%56.11%24.83%7.72%8.86%0.593
3218.60%0.57%0.19%0.13%0.00%0.26%55.03%25.23%7.85%8.89%0.605
3319.23%0.58%0.19%0.14%0.00%0.29%53.94%25.64%7.98%8.93%0.617
3419.85%0.59%0.20%0.14%0.00%0.33%52.85%26.04%8.11%8.97%0.629
3520.48%0.60%0.21%0.15%0.00%0.36%51.76%26.44%8.24%9.01%0.640
3621.11%0.61%0.21%0.16%0.00%0.39%50.66%26.85%8.37%9.05%0.652
3721.74%0.62%0.22%0.17%0.00%0.44%49.56%27.25%8.49%9.09%0.663
3822.37%0.64%0.23%0.17%0.00%0.48%48.46%27.65%8.62%9.13%0.674
3923.00%0.65%0.24%0.18%0.00%0.53%47.35%28.05%8.75%9.17%0.685
4023.63%0.66%0.25%0.19%0.00%0.58%46.23%28.45%8.88%9.21%0.696
4124.27%0.67%0.25%0.20%0.00%0.65%45.11%28.85%9.01%9.26%0.706
4224.90%0.68%0.26%0.21%0.00%0.71%43.99%29.25%9.14%9.30%0.717
4325.53%0.69%0.27%0.22%0.00%0.78%42.86%29.65%9.26%9.34%0.727
4426.17%0.70%0.28%0.23%0.00%0.86%41.72%30.04%9.39%9.39%0.737
4526.80%0.71%0.28%0.24%0.00%0.94%40.58%30.44%9.52%9.44%0.747
4627.44%0.72%0.29%0.25%0.00%1.03%39.43%30.83%9.65%9.48%0.757
4728.07%0.73%0.30%0.26%0.00%1.11%38.30%31.23%9.77%9.53%0.766
4828.71%0.74%0.31%0.27%0.00%1.19%37.16%31.62%9.90%9.58%0.776
4929.34%0.76%0.32%0.28%0.00%1.27%36.02%32.01%10.03%9.63%0.785
5029.98%0.77%0.32%0.29%0.00%1.35%34.88%32.41%10.16%9.68%0.794
5130.62%0.78%0.33%0.30%0.00%1.43%33.74%32.80%10.28%9.73%0.803
5231.25%0.79%0.34%0.31%0.00%1.52%32.59%33.19%10.41%9.78%0.812
5331.89%0.80%0.35%0.33%0.00%1.61%31.44%33.58%10.54%9.83%0.821
5432.52%0.81%0.36%0.34%0.00%1.70%30.29%33.98%10.66%9.88%0.829
5533.15%0.82%0.37%0.35%0.00%1.79%29.15%34.36%10.79%9.93%0.838
5633.79%0.83%0.38%0.36%0.00%1.86%28.02%34.75%10.92%9.98%0.846
5734.41%0.84%0.39%0.38%0.00%1.93%26.91%35.15%11.04%10.04%0.854
5835.03%0.85%0.40%0.39%0.00%1.98%25.81%35.54%11.17%10.09%0.862
5935.65%0.86%0.41%0.41%0.00%2.04%24.71%35.92%11.30%10.14%0.870
6036.27%0.87%0.43%0.42%0.00%2.10%23.61%36.30%11.42%10.20%0.878
6136.89%0.87%0.44%0.44%0.00%2.14%22.54%36.69%11.55%10.25%0.886
6237.50%0.89%0.46%0.45%0.00%2.18%21.47%37.06%11.67%10.30%0.893
6338.11%0.90%0.47%0.47%0.00%2.23%20.40%37.42%11.79%10.36%0.900
6438.73%0.92%0.49%0.48%0.00%2.27%19.33%37.78%11.92%10.41%0.907
6539.35%0.93%0.50%0.50%0.00%2.31%18.29%38.13%12.04%10.47%0.914
6639.97%0.95%0.51%0.51%0.00%2.35%17.24%38.47%12.16%10.52%0.921
6740.58%0.97%0.53%0.53%0.00%2.37%16.22%38.81%12.28%10.58%0.928
6841.18%0.99%0.54%0.55%0.00%2.37%15.22%39.15%12.40%10.63%0.934
6941.79%1.02%0.55%0.56%0.00%2.38%14.23%39.48%12.53%10.69%0.941
7042.38%1.04%0.57%0.58%0.00%2.37%13.25%39.80%12.65%10.75%0.947
7142.97%1.07%0.58%0.61%0.00%2.33%12.32%40.13%12.76%10.80%0.953
7243.56%1.09%0.59%0.63%0.00%2.27%11.41%40.45%12.88%10.86%0.959
7344.16%1.12%0.60%0.65%0.00%2.21%10.50%40.77%13.00%10.92%0.965
7444.74%1.15%0.61%0.68%0.00%2.14%9.62%41.07%13.12%10.97%0.971
7545.30%1.19%0.62%0.70%0.00%2.06%8.77%41.36%13.24%11.03%0.976
7645.84%1.26%0.63%0.72%0.00%1.98%7.96%41.61%13.35%11.08%0.981
7746.34%1.35%0.64%0.76%0.00%1.87%7.20%41.83%13.45%11.14%0.986
7846.83%1.45%0.65%0.80%0.00%1.75%6.47%42.03%13.55%11.19%0.990
7947.30%1.55%0.67%0.87%0.01%1.64%5.76%42.20%13.65%11.24%0.994
8047.77%1.65%0.68%0.94%0.00%1.53%5.11%42.32%13.74%11.29%0.998
8148.25%1.75%0.69%1.02%0.00%1.39%4.51%42.39%13.83%11.34%1.002
8248.77%1.83%0.70%1.11%0.00%1.26%3.95%42.38%13.92%11.39%1.005
8349.22%1.91%0.71%1.20%0.00%1.13%3.44%42.38%13.99%11.44%1.007
8449.65%2.01%0.72%1.28%0.00%1.03%2.96%42.35%14.06%11.48%1.010
8550.05%2.15%0.73%1.37%0.00%0.92%2.50%42.27%14.13%11.53%1.012
8650.50%2.31%0.73%1.46%0.00%0.80%2.11%42.09%14.19%11.57%1.013
8750.78%2.52%0.74%1.56%0.00%0.69%1.75%41.94%14.24%11.61%1.014
8850.96%2.75%0.75%1.67%0.00%0.58%1.45%41.84%14.28%11.65%1.014
8951.05%2.99%0.76%1.81%0.00%0.49%1.18%41.73%14.31%11.68%1.014
9051.13%3.24%0.75%1.95%0.00%0.42%0.93%41.58%14.34%11.71%1.013
9151.19%3.53%0.72%2.07%0.00%0.35%0.72%41.43%14.36%11.74%1.013
9251.24%3.87%0.69%2.21%0.00%0.28%0.52%41.19%14.38%11.77%1.011
9351.32%4.22%0.64%2.36%0.00%0.21%0.35%40.91%14.39%11.81%1.010
9451.37%4.58%0.61%2.50%0.00%0.15%0.22%40.57%14.40%11.84%1.008
9551.33%4.96%0.59%2.63%0.00%0.10%0.12%40.28%14.40%11.86%1.005
9650.98%5.44%0.57%2.83%0.00%0.06%0.06%40.05%14.38%11.89%1.002
9749.98%6.22%0.60%3.07%0.00%0.04%0.03%40.06%14.34%11.91%0.997
9848.90%7.01%0.66%3.38%0.00%0.02%0.01%40.01%14.28%11.93%0.991
9947.90%7.67%0.61%3.91%0.00%0.01%0.00%39.90%14.23%11.95%0.984
10047.00%8.00%0.50%5.00%0.00%0.00%0.00%39.50%14.17%11.97%0.977
*Annualized ex-ante values shown for portfolio return and volatility. Ex-ante Sharpe Ratio calculated using historical U.S. 3-Month Treasury Bill Rate returns as the risk-free rate.

  • IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
  • The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities. All use is subject to terms of service.
  • Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
  • Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
  • Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
  • The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete. Other investments not considered may have characteristics similar or superior to those being analyzed.
  • Refer to the related documentation sections for more details on terms and definitions, methodology, and data sources.
  • Portfolio optimization is a process of choosing the proportions of various assets to be held in a portfolio in such a way as to make the portfolio better than any other combination according to the selected objective function such as maximizing risk-adjusted return. Portfolio optimization determines target weights for portfolio assets based on mathematical models that can use either historical or forecasted data as inputs. Optimization results are not guarantees of future performance.
  • The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
  • Historical asset statistics are based on monthly returns from Jan 2017 to Sep 2026
  • The efficient frontier is based on the monthly returns, volatilities, and correlations of the specified assets
  • Monte Carlo method was used to resample the efficient frontier inputs to mitigate the impact of input estimation errors
  • The displayed standard deviation and expected return in the efficient frontier are annualized from the monthly returns
  • Ex-ante Sharpe Ratio for the efficient frontier data points is calculated using historical U.S. 3-Month Treasury Bill Rate returns as the risk free rate